The ratio of the length of a column to the minimum radius of gyration of its cross-sectional area is known as:
Try it first: pick an option, then read the explanation.
Correct answer: A. slenderness ratio
Asked in SSC JE 25/01/2018 (Morning)
Detailed Explanation
Slenderness measures how prone a column is to buckling: long and thin means high slenderness.
\[ \lambda = \frac{l_e}{r_{min}}, \qquad r_{min} = \sqrt{\frac{I_{min}}{A}}, \qquad \sigma_{cr} = \frac{\pi^2E}{\lambda^2} \]
Why “slenderness ratio” Is Correct
The ratio is the slenderness ratio. (Strictly the effective length is used.)
| Term | Meaning |
|---|---|
| Radius of gyration r | r = √(I/A); use the least value rmin = √(Imin/A) for buckling |
| Slenderness ratio λ | λ = le / rmin |
| Euler stress | σcr = P/A = π²E/λ² |
| Short column / pedestal | le / least lateral dimension ≤ 3 (fails by crushing) |
| Long column | Large λ; fails by buckling — Euler's formula applies |
Why the Other Options Are Wrong
- B. buckling ratio: "Buckling ratio" is not a standard term.
- C. crippling ratio: "Crippling ratio" is not a standard term.
- D. compressive ratio: "Compressive ratio" is not a standard term.
Key Point
Slenderness ratio λ = effective length / least radius of gyration.
Key Concepts for Students
- High λ → buckling governs; low λ → crushing governs.
- IS 800 limits λ to 180 for compression members carrying dead and imposed loads.
- Euler critical stress falls with the square of λ.
Practice more: this is question 11 in Columns and Struts MCQs – Part 1. Try the whole set and check every answer instantly.